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A014649 Number of partitions of n into its nonprime power divisors with at least one part of size 1. 3
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 6, 1, 1, 1, 2, 1, 15, 1, 1, 1, 1, 1, 16, 1, 1, 1, 6, 1, 21, 1, 2, 3, 1, 1, 26, 1, 5, 1, 2, 1, 18, 1, 6, 1, 1, 1, 238, 1, 1, 3, 1, 1, 31, 1, 2, 1, 31, 1, 139, 1, 1, 5, 2, 1, 37, 1, 26, 1, 1, 1, 414, 1, 1, 1, 6, 1, 612, 1, 2, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,12

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..20000

David A. Corneth & Antti Karttunen, PARI program

PROG

(PARI)

\\ This is for computing a small number of terms:

nonprimepower_divisors_with1_reversed(n) = vecsort(select(d -> ((1==d) || !isprimepower(d)), divisors(n)), , 4);

partitions_into_with_trailing_ones(n, parts, from=1) = if(!n, 1, if(#parts<=(from+1), if(#parts == from, 1, (1+(n\parts[from]))), my(s=0); for(i=from, #parts, if(parts[i]<=n, s += partitions_into_with_trailing_ones(n-parts[i], parts, i))); (s)));

A014649(n) = partitions_into_with_trailing_ones(n-1, nonprimepower_divisors_with1_reversed(n)); \\ Antti Karttunen, Aug 23 2019

(PARI) \\ For an efficient program to compute large numbers of terms, see PARI program included in the Links-section.

CROSSREFS

Cf. A014648, A014650, A014651, A014652, A066874.

Sequence in context: A062760 A323163 A322318 * A326568 A279817 A309386

Adjacent sequences:  A014646 A014647 A014648 * A014650 A014651 A014652

KEYWORD

nonn

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified July 10 15:45 EDT 2020. Contains 335577 sequences. (Running on oeis4.)